The general linear model (GLM) has been extensively applied to fMRI data in the time domain. However, traditionally
time series data can be analyzed in the Fourier domain where the assumptions made as to the noise in the signal can be
less restrictive and statistical tests are mathematically more rigorous. A complex form of the GLM in the Fourier domain
has been applied to the analysis of fMRI (BOLD) data. This methodology has a number of advantages over temporal
methods: 1. Noise in the fMRI data is modeled more generally and closer to that actually seen in the data. 2. Any input
function is allowed regardless of the timing. 3. Non-parametric estimation of the transfer functions at each voxel are
possible. 4. Rigorous statistical inference of single subjects is possible. This is demonstrated in the analysis of an
experimental design with random exponentially distributed stimulus inputs (a two way ANOVA design with input
stimuli images of alcohol, non-alcohol beverage and positive or negative images) sampled at 400 milliseconds. This
methodology applied to a pair of subjects showed precise and interesting results (e.g. alcoholic beverage images
attenuate the response of negative images in an alcoholic as compared to a control subject).